Well no, historians examine the causes of events, as gleaned from the sources available to them. So if Unwin were right we should expect to see his ideas reflected in historical theories.
As has been pointed out, the (Western) Roman empire fell for other reasons, after Christianity had been adopted as the official religion. And besides, who is to say that the fall of the empire indicated any deterioration in the society? Perhaps it improved, became less bloodthirsty and brutal. Nowadays we frown on imperialism, don’t we?
And going - for the sake of argument- by the rather fascist yardstick of empire as a measure of social vitality, there are plenty of other counterexamples, for instance the USSR.
Or, to look as other religious societies today , do we think Iran, Saudi Arabia, or Afghanistan, are model societies we should strive to emulate?